MODULE 1.2: Time-Weighted and Money-Weighted Returns

Question 1

Money-weighted return definition

Answer 1

applies the internal rate of return (IRR) concept to investment portfolios. IRR is the interest rate that makes the present value of all cash inflows equal to the present value of all cash outflows—resulting in a net present value (NPV) of zero

This is really sensitive to the time at which the investment is made. If you invest right before the market dips, this would show a smaller return.

Question 2

Money-weighted return formula/calculator keys

Answer 2

Calculator key:
1. press CF key
2. enter CF0 which is the initial investment
3. Enter subsequent cash flows using CF key for each period
4. Press IRR and then CPT to compute the internal rate of return
5. make sure to include positives and negatives for cash inflows and outflows from portfolios. You could choose which one you want to be negative.

1. For example, if we are talking from the perspective of the brokerage account , the purchase of a share would be + while me giving out dividends would be negative.

Question 3

The time-weighted rate of return definition

Answer 3

This shows the time controlled return of a portfolio. For example, we control for the time at which the portfolio invests money. If there is an investment made at a time right when the market drops, this timing shouldn’t effect the returns. This is the standard.

Question 4

The time-weighted rate of return CALCULATION

Answer 4

1. calculate the holding period values for each period
2. calculate the HPR for each period
3. do (1+HPR1)x(1+HPR2)……x(1+HPR) as many times as there are periods
4. take the holding period number root and -1 (2 periods = square root)
5. DIVIDENDS ONLY IN NUMERATOR OF THE HPR here

Question 5

When is the time weighted average preferred and when is the money weighted preferred?

Answer 5

1. money weighted = if a manager has full control over cash flows in and out of an account, the money-weighted rate of return becomes the more suitable performance measure.
2. time weighted = if manager doesn’t have control over timing. Time weighted > if you invest right before poor market conditions.

Question 6

An investor buys a share of stock for $40 at time t = 0, buys another share of the same stock for $50 at t = 1, and sells both shares for $60 each at t = 2. The stock paid a dividend of $1 per share at t = 1 and at t = 2. The periodic money-weighted rate of return on the investment is closest to:

Answer 6

Using the cash flow functions on your financial calculator, enter CF0 = –40; CF1 = –50 + 1 = –49; CF2 = 60 × 2 + 2 = 122; and CPT IRR = 23.82%.

Question 7

An investor buys a share of stock for $40 at time t = 0, buys another share of the same stock for $50 at t = 1, and sells both shares for $60 each at t = 2. The stock paid a dividend of $1 per share at t = 1 and at t = 2. The time-weighted rate of return on the investment for the period is closest to:

Answer 7

HPR1 =(50 + 1 / 40 ) - 1= 27.5%
HPR2 = (120 + 2 / 100) - 1 = 22.0%
TWR = SQRT (1+ .275) (1 + .22) = 24.72%

Question 8

On January 1, Jonathan Wood invests $50,000. At the end of March, his investment is worth $51,000. On April 1, Wood deposits $10,000 into his account, and by the end of June, his account is worth $60,000. Wood withdraws $30,000 on July 1 and makes no additional deposits or withdrawals the rest of the year. By the end of the year, his account is worth $33,000. The time-weighted return for the year is closest to:

Answer 8

January – March return = 51,000 / 50,000 − 1 = 2.00%

April – June return = 60,000 / (51,000 + 10,000) − 1 = –1.64%

July – December return = 33,000 / (60,000 − 30,000) − 1 = 10.00%

Time-weighted return = [(1 + 0.02)(1 − 0.0164)(1 + 0.10)] − 1 = 0.1036 or 10.36%

INVESTMENT SPANS ONLY 1 YEAR!!!!